What was meant by the phrase: “Do the work of an evangelist”?
Timothy’s primary function or area of giftedness was not evangelism, but Paul challenged him to “do the work of an evangelist,” (cf. 1 Tim. 4:12). I think the command to “do the work of an evangelist” simply expressed Paul’s concern that Timothy might not lose his zeal for lost souls as he became more and more engrossed in his primary duties. Perhaps it also expressed the apostle’s concern that evangelism be illustrated and communicated to those he was training. They too need this concern, training, and skill as part of their growth. Part of the job of equipping others for ministry and the growth of the body of Christ (qualitatively, quantitatively, and organically) would be the need to teach and model personal evangelism (cf. Eph. 4:11f).
The principle here is true with many, though not all, of the gifts God has given believers. All do not have the gifts of faith, giving, showing mercy, and helps, which are specific gifts mentioned in the New Testament, but certainly we are all to have faith, give, show mercy, and help others. Some, however, are uniquely able to serve in these capacities above the norm. I think the same applies to the gift of evangelism.